Question

Find the power series representation centered at x=0 of the following function:

F(x) = 1/(1+2(x^2))

Answer 1

easy way may be to start with
\[\frac{1}{1-x}=1+x+x^2+...=\sum_{k=0}^{\infty}x^k\] and rework
\[\frac{1}{1+2x^2}\] so look like that

Answer 2

\[\frac{1}{1+x}=1-x+x^2-x^3+...=\sum_{k=0}^{\infty}(-1)^kx^k\]
\[\frac{1}{1+x^2}=1-x^2+x^4-...=\sum_{k=0}^{\infty}(-1)^kx^{2k}\] one more and you are done

Answer 3

so it should look something like this then??
\[\sum_{n=0}^{\infty } (-1)^{n} (1/2n)(x^{2n}) \]

Answer 4

or maybe that (1/2n) should be 1/(n+1)